“covariance”的概念、定义、翻译、参考文献-科学参考

covariance

Physics

A statistic that measures the association between two variables. If for x and y there are n pairs of values (x_i, y_i), then the covariance is defined as

$[1 / (n - 1)] Σ (x_{i} - x') (y_{i} - y')$

where x′ and y′ are the mean values.

Mathematics

The covariance of two random variables X and Y, denoted by Cov(X, Y), is equal to E((X − μ‎_X)(Y − μ‎_Y)), where μ‎_X and μ‎_Y are the population means of X and Y respectively (see expected value). If X and Y are independent random variables, then Cov(X, Y)=0. For computational purposes, note E((X − μ‎_X)(Y −μ‎_Y))=E(XY) − μ‎_X μ‎_Y. For a sample of n paired observations (x₁, y₁), (x₂, y₂),…, (x_n, y_n), the sample covariance is equal to

$\frac{∑ (x_{i} - \bar{x}) (y_{i} - \bar{y})}{n} .$

Statistics

A term used to refer to either the population covariance or the sample covariance, depending on context.

Computer

A measure of the joint variation of two random variables, analogous to variance (see measures of variation). If the variables are x and y then the covariance of x and y is
$Σ (x_{i} - \bar{x}) (y_{i} - \bar{y})$
The analysis of covariance is an extension of the analysis of variance in which the variables to be tested are adjusted to take account of assumed linear relationships with other variables. See also correlation.

Geology and Earth Sciences

In statistics, a measure of the association between two variables. Covariance is calculated as the difference between the average product of corresponding values in the two data sets and the product of the means of the two data sets. A value of zero indicates no relationship between the data sets. The covariance value can be used to calculate linear regression and principal components.

Economics

A measure of the degree of linear relationship between two random variables, say, X and Y, defined by

$C o v (X, Y) = E [(X - E [X]) (Y - E [Y])] .$

Positive (negative) covariance means that large values of X are likely to be observed with large (small) values of Y.

单词	covariance
释义	covariance Physics A statistic that measures the association between two variables. If for x and y there are n pairs of values (x_i, y_i), then the covariance is defined as $[1 / (n - 1)] Σ (x_{i} - x') (y_{i} - y')$ where x′ and y′ are the mean values. Mathematics The covariance of two random variables X and Y, denoted by Cov(X, Y), is equal to E((X − μ‎_X)(Y − μ‎_Y)), where μ‎_X and μ‎_Y are the population means of X and Y respectively (see expected value). If X and Y are independent random variables, then Cov(X, Y)=0. For computational purposes, note E((X − μ‎_X)(Y −μ‎_Y))=E(XY) − μ‎_X μ‎_Y. For a sample of n paired observations (x₁, y₁), (x₂, y₂),…, (x_n, y_n), the sample covariance is equal to $\frac{∑ (x_{i} - \bar{x}) (y_{i} - \bar{y})}{n} .$ Statistics A term used to refer to either the population covariance or the sample covariance, depending on context. Computer A measure of the joint variation of two random variables, analogous to variance (see measures of variation). If the variables are x and y then the covariance of x and y is $Σ (x_{i} - \bar{x}) (y_{i} - \bar{y})$ The analysis of covariance is an extension of the analysis of variance in which the variables to be tested are adjusted to take account of assumed linear relationships with other variables. See also correlation. Geology and Earth Sciences In statistics, a measure of the association between two variables. Covariance is calculated as the difference between the average product of corresponding values in the two data sets and the product of the means of the two data sets. A value of zero indicates no relationship between the data sets. The covariance value can be used to calculate linear regression and principal components. Economics A measure of the degree of linear relationship between two random variables, say, X and Y, defined by $C o v (X, Y) = E [(X - E [X]) (Y - E [Y])] .$ Positive (negative) covariance means that large values of X are likely to be observed with large (small) values of Y.
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